How do we measure the marginal physical product of a variable factor of production?
Answer:
In his discussions of the Law of Diminishing Returns, Malthus did not distinguish between average and marginal productivity. However, in modern economics, we think of diminishing returns primarily in terms of marginal, not average, productivity. Thus, we would state the law this way:
Law of Diminishing Returns (Modern Statement):
When the technology of production and some of the inputs are held constant and the quantity of a variable input increases continually, the marginal productivity of the variable input will eventually decline.
The inputs that are held steady are called the "fixed inputs." In these pages we are treating land and capital as fixed inputs. The inputs that are allowed to vary are called the "variable inputs." In these pages we are treating labor as the variable input.
Another way to express the law of diminishing returns, is that, as the variable input increases, the output also increases, but at a decreasing rate. The marginal productivity of labor is the rate of increase in output as the labor input increases. To say that output increases at a decreasing rate when the variable input increases is another way to say that the marginal productivity declines. Let's extend the numerical example in the page before last and see how marginal productivity varies over a wide range of labor inputs. Here is a hypothetical example of production with the inputs of land and labor held steady and varying quantities of labor, and the output and average and marginal productivities.
Table 1
Read the 4 numbers in the follwing order: Labor, Output , Average Productivity, Marginal Productivity
0 0 0 9.45
100 945 9.45 8.35
200 1780 8.90 7.25
300 2505 8.35 6.15
400 3120 7.80 5.05
500 3625 7.25 3.95
600 4020 6.70 2.85
700 4305 6.15 1.75
800 4480 5.60 0.65
900 4545 5.05 -0.45
1000 4500 4.500
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a simple example to explain the law of diminishing returns to students‑‑sweeping the classroom floor. I usually start by stating the law as simply as possible. Then I tell the class that we have the job of sweeping the floor. All students agree that they are interchangeable when it comes to sweeping. They can all sweep and all can sweep equally well. I ask them how to measure our efficiency, if all sweep equally well. The general response is that we can measure efficiency in terms of time. Then I explain that we have four brooms and I will choose people to serve as sweepers. I choose the first sweeper and tell him it will take 60 minutes to do the job. The use of 60 minutes is for easy division. If you must, you can remind the students that the job was never done before so we have no idea how long it will take to complete the job. A second student is chosen and I ask how long it will take with two sweepers. The response is thirty minutes. Questions may be asked to explain the thirty minute time. After a third sweeper is added the time falls to twenty minutes. A fourth sweeper brings the time to fifteen minutes. Then I add a fifth sweeper and ask for the time. Twelve minutes will be given as the logical answer. Now I explain that twelve minutes is incorrect, and that it will take twenty‑four minutes. I ask the students to explain why it took longer with five sweepers than with four. Most of the class will quickly point out that we only have four brooms. Then I restate the law of diminishing returns stressing that sweepers are inputs, brooms are the fixed factors, and the amount of time reflects marginal returns.
Diminishing returns is not always applicable. For some levels of additional doses of a variable input, there may be increasing marginal physical productivity, but after a while diminishing returns starts. There are also cases of constant returns where all variable inputs have to be increased in certain fixed proportions.
You may bot know what is the marginal physical productivity in advance. You have to go on increasing the doses of the a variable input factor at different trials and measure the total output. Form the total outputs recorded at different level of doses of the variable input, you can finf the marginal physical productivity at successive level of higher doses.When you have lot of statistical data to estimate the production function, you can use differentian (calculus) to estmate the marginal productivity at different doses of a variable factor.
Imagine a simple thought experiment. Hold all the inputs of your business but one constant, say labor. Now, add a unit of labor, and see how much output you get. Keep adding units of labor, from say 1 to 10, and record how much output you get , say 8 to 1000, whatever. Then, generate a column which is the change in output for each increase in labor unit. This column is the 'marginal physical product'.
Now ask yourself, what would the output series look like? What would the change in the output series look like?
Take an example like a university, with teachers being the input, and educated students being the output. What happens to educated students as you begin to have one, two, three, 30, 50, 1000, a million teachers? Remember, the number of students, buildings and land is all fixed.
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